WRITING EXPRESSIONS INVOLVING PERCENT INCREASE AND DECREASE

Recall that whenever you see the percent symbol, $\,\%\,$, you can trade it in for a multiplier of $\frac{1}{100}$.
(Indeed, per-cent means per-one-hundred.)

For example, $\,20\%\,$ goes by all these names: $$\,20\% = 20\cdot\frac{1}{100}= \frac{20}{100} = \frac{2}{10} = \frac{1}{5} = 0.2$$

In particular, note that $\,100\% = 100\cdot\frac{1}{100} = 1\,$,
so $\,100\%\,$ is just another name for the number $\,1\,$.

Also recall that it's easy to go from percents to decimals:
just move the decimal point two places to the left.
For example:   $\,20\% = 20.\% = 0.20$
It's good style to put a zero in the ones place (i.e., write $\ 0.20\$, not $\ .20\$).

To change from decimals to percents,
just move the decimal point two places to the right.
For example:   $0.2 = 0.20 = 20.\% = 20\%$

The ‘Puddle Dipper’ memory device may be useful to you:
PuDdLe: to change from Percents to Decimals, move the decimal point two places to the Left.
DiPpeR: to change from Decimals to Percents, move the decimal point two places to the Right.

EXAMPLES:

Here, you will practice writing expressions involving percent increase and decrease, and related concepts.

Another name for the expression ‘$\,20\%\text{ of } x\,$’ is:   $0.2x$
Why? The mathematical word ‘of ’ indicates multiplication, so:
$\,(20\%\text{ of } x) = (20\%)(x) = (0.2)(x) = 0.2x\,$.
Another name for the expression ‘$\,100\%\text{ of } x\,$’ is:   $x$
Another name for the expression ‘$\,300\%\text{ of } x\,$’ is:   $3x$
If $\,x\,$ increases by $\,20\%\,$, then the new amount is:   $x + 0.2x = 1x + 0.2x = 1.2x$
If $\,x\,$ has a $\,20\%\,$ increase, then the new amount is:   $1.2x$
If $\,x\,$ increases by $\,47\%\,$, then the new amount is:   $x + 0.47x = 1.47x$
If $\,x\,$ decreases by $\,30\%\,$, then the new amount is:   $x - 0.3x = 1x - 0.3x = 0.7x$
If $\,x\,$ has a $\,30\%\,$ decrease, then the new amount is:   $0.7x$
If $\,x\,$ increases by $\,100\%\,$, then the new amount is:   $x + x = 1x + 1x = 2x$
If $\,x\,$ increases by $\,182\%\,$, then the new amount is:   $x + 1.82x = 2.82x$
If $\,x\,$ increases by $\,200\%\,$, then the new amount is:   $x + 2x = 3x$
If $\,x\,$ doubles, then the new amount is:   $2x$
If $\,x\,$ triples, then the new amount is:   $3x$
If $\,x\,$ quadruples, then the new amount is:   $4x$
If $\,x\,$ is halved, then the new amount is:   $\displaystyle\frac{1}{2}x = 0.5x$
Master the ideas from this section